Simplify the following expression: $x = \dfrac{-8n^2 + 16n + 192}{n - 6} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-8$ , so we can rewrite the expression: $ x =\dfrac{-8(n^2 - 2n - 24)}{n - 6} $ Then we factor the remaining polynomial: $n^2 {-2}n {-24} $ ${-6} + {4} = {-2}$ ${-6} \times {4} = {-24}$ $ (n {-6}) (n + {4}) $ This gives us a factored expression: $\dfrac{-8(n {-6}) (n + {4})}{n - 6}$ We can divide the numerator and denominator by $(n + 6)$ on condition that $n \neq 6$ Therefore $x = -8(n + 4); n \neq 6$